Rabbi Soloveichik's argument: "if the Talmud debated whether the fast starts at night, and some later rabbis thought you start saying the fast-day prayers at night, that means that elements of the fast really start at night."

Rabbi Feinstein's argument (OC I:168): "the Talmud concludes that the fast doesn't start at night; yes it was later debated about saying the prayers at night, but we conclude that the fast-day prayers don't start until day; that opinion has stronger Talmudic support; and the whole no-three-weeks-wedding thing is a custom, so we should be lenient in cases of doubt."

On the surface level, yes, but more importantly is whether one should. The three weeks are a rather auspicious time and over the centuries Jews have tried to prevent taking on major activities during that time. My recommendation would be to hold off until after 9th of Av, the 15th is especially an auspicious day to get married. There are also questions of sheva brachos during the three weeks, one can have them, but again, the mood is not ideal and has certain overtones. Its probably ideal to delay if possible, otherwise, its not asur.

"On the surface level, yes": Do you have a source for this?
–
msh210♦Jun 28 '11 at 1:46

@msh210, why do you necessarily assume that something must be forbidden?
–
Adam MoshehJan 31 '12 at 5:43

@Adam, I don't assume things are forbidden with no basis. In this case, though, there's a widespread practice that we don't marry in the three weeks, and night generally counts as part of the next day in Judaism.
–
msh210♦Jan 31 '12 at 5:54

There is a discussion among the poskim if one has to refrain from the actions which are
not done during the three weeks from the morning of Shiva Asar B’tamuz or even the night
before? Most poskim say that one should refrain from doing these activities even from
the night before, from tzeis. In a pressing situation one can be lenient (i.e. wedding on
Motzei Shabbos).11

From Footnote 11: "...This is even with music etc (See Igros Moshe E.H. 1:97)

And:

The custom of Ashkenazim is to refrain from making weddings from the night of
Shiva Asar B’tamuz until after Tisha B’av. This is even if one has not fulfilled the mitzvah of having children.

There was a big fight over this in Israel, I believe during the 70's / 80's. The chief rabbinate was dominated by Ashkenazim and they forbade weddings during the three weeks. One of the many things Rav. Ovadia Yosef is known for was his fight for Sephardi traditions, one of which is that weddings are allowed during the three weeks:

As a leading Sephardic Torah scholar and arbiter of halakha, Rabbi
Yosef was often described by his followers as the greatest of the
generation and the outstanding Sephardic rabbinical authority of the
century. His most outstanding quality was his courage to proudly renew
the Sephardic system of legislation. Time and again he disagreed,
openly and proudly, with the official position of the rabbanut, while
sticking to his religious Sephardic position. Thus, for example, when
he was the Chief Rabbi of Tel Aviv, he cancelled the religious
council’s decision not to permit marriage in the Ben Hametzarim (three
weeks) days—as the Ashkenazim do—and instructed all the marriage
registrars in his jurisdiction to allow marriage of Sephardic Jews for
the whole month of Tamuz.